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Optics and Spectroscopy

Controlling qubit transitions through quantum interference during nonadiabatic rapid passage

Ruihu Li, Frank Gaitan

Published Aug 1, 2005• 6 citations
Publisher

Abstract

We provide a further exploration of a type of nonadiabatic rapid passage known as twisted rapid passage (TRP). This class of rapid passage pulses allows a qubit to be driven through resonance multiple times during a single TRP sweep. The multiple resonances give rise to controllable quantum interference effects that provide direct control over qubit transitions so that transitions can be greatly enhanced or suppressed. These quantum interference effects have recently been observed experimentally. We examine here a number of new TRP pulse profiles and show that they can be used to implement a quantum NOT gate that operates both nonadiabatically and with sufficient reliability to surpass the accuracy threshold needed for the gate to be used as part of a fault-tolerant scheme of quantum computation. These new TRP pulse profiles are shown to provide performance advantages over TRP pulses previously considered in the literature.

DOI
10.1134/1.2034612

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We provide a further exploration of a type of nonadiabatic rapid passage known as twisted rapid passage (TRP). This class of rapid passage pulses allows a qubit to be driven through resonance multiple times during a single TRP sweep. The multiple resonances give rise to controllable quantum interference effects that provide direct control over qubit transitions so that transitions can be greatly enhanced or suppressed. These quantum interference effects have recently been observed experimentally. We examine here a number of new TRP pulse profiles and show that they can be used to implement a quantum NOT gate that operates both nonadiabatically and with sufficient reliability to surpass the accuracy threshold needed for the gate to be used as part of a fault-tolerant scheme of quantum computation. These new TRP pulse profiles are shown to provide performance advantages over TRP pulses previously considered in the literature.
In adiabatic rapid passage, the Bloch vector of a qubit is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In non-adiabatic twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle φ(t) at the same time that it is non-adiabatically inverted. For polynomial twist, φ(t) ∼ Bt n . We show that, for n ≥ 3, multiple qubit resonances can occur during a single inversion of the external field, producing strong interference effects in the qubit transition probability. The character of the interference is controllable through variation of the twist strength B. Both constructive and destructive interference are possible, allowing qubit transitions to be greatly enhanced or suppressed. Experimental confirmation of these controllable interference effects has already occurred. Application of this interference mechanism to the construction of fast fault-tolerant quantum controlled-NOT and NOT gates is discussed.
Twisted rapid passage is a type of non-adiabatic rapid passage that gives rise to controllable quantum interference effects that were first observed experimentally in 2003. We show that twisted rapid passage sweeps can be used to implement a universal set of quantum gates that operate with high-fidelity. For each gate in the universal set, sweep parameter values are provided which simulations indicate will yield a quantum gate with error probability P_{e} < 10**(-4). Note that all gates in this universal set are driven by a **single** type of control field (twisted rapid passage), and the error probability for each gate falls below the rough-and-ready estimate for the accuracy threshold P_{a} ~ 10**(-4). The simulations suggest that the universal gate set produced by twisted rapid passage shows promise for use in a fault-tolerant scheme for quantum computing.
In adiabatic rapid passage, the Bloch vector of a qubit is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In non-adiabatic twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle \\phi(t) at the same time that it is non-adiabatically inverted. For polynomial twist, \\phi(t) \\sim Bt^{n}. We show that for n \\ge 3, multiple qubit resonances can occur during a single inversion of the external field, producing strong interference effects in the qubit transition probability. The character of the interference is controllable through variation of the twist strength B. Constructive and destructive interference are possible, greatly enhancing or suppressing qubit transitions. Experimental confirmation of these controllable interference effects has already occurred. Application of this interference mechanism to the construction of fast fault-tolerant quantum CNOT and NOT gates is discussed.
In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $\ensuremath{\varphi}(t)$ at the same time that it is inverted. For polynomial twist, $\ensuremath{\varphi}(t)\ensuremath{\sim}{\mathrm{Bt}}^{n}.$ We show that for n> 3,n>~3,n> 3, multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength B, which can be used to control the time separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wave function. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum controlled-NOT and NOT gates is discussed.
Twisted rapid passage is a type of non-adiabatic rapid passage that generates controllable quantum interference effects that were first observed experimentally in 200320032003. It is shown that twisted rapid passage sweeps can be used to implement a universal set of quantum gates $\calGU$ that operate with high-fidelity. The gate set $\calGU$ consists of the Hadamard and NOT gates, together with variants of the phase, π/8\pi /8π/8, and controlled-phase gates. For each gate ggg in $\calGU$, sweep parameter values are provided which simulations indicate will produce a unitary operation that approximates ggg with error probabilityPe<10−4P_{e} < 10^{-4}Pe​<10−4. Note that \textit{all\/} gates in $\calGU$ are implemented using a \textit{single family\/} of control-field, and the error probability for each gate falls below the rough-and-ready estimate for the accuracy threshold Pa∼10−4P_{a}\sim 10^{-4}Pa​∼10−4.
In this thesis, details are presented of a numeric simulation of non-adiabatic rapid passage sweeps that were first realized experimentally in 1991. The sweeps are non-composite and generate controllable interference effects which can be used to create high accuracy quantum gates. The simulation is used to optimize the sweep parameters in order to obtain a reliable set of one-qubit quantum gates. A set of sweep parameters was found that approximate the Hadamard, a modified pi/8, a modified phase, and the not gates with an error probability of less than 10^-4. These gates are significant because they form a set that can approximate an arbitrary one qubit unitary operation. The 10^-4 is also significant because is used a rough estimate for the accuracy required to implement fault-tolerant quantum logic.